Abstract
By starting from the one-parameter Modified Borel-Tanner distribution proposed recently in the statistic literature, we introduce the zero-inflated Modified Borel-Tanner distribution. Additionally, on the basis of the proposed zero-inflated distribution, a novel zero-inflated regression model is proposed, which is quite simple and may be an interesting alternative to usual zero-inflated regression models for count data. The parameters of the proposed model are estimated by Maximum Likelihood Estimation technique. To check the potentiality of the zero inflated Modified Borel-Tanner regression, an application to the count of infected blood cells is taken. The results suggest that the new zero inflated Modified Borel-Tanner regression is more appropriate to model these count data than other familiar zero-inflated (or not) regression models commonly used in practice.
Highlights
Without any ambiguity, Poisson model is one of the basic and simplest count data model and most common in practice to deal with count data
The Poisson model assumes that the events taken into consideration occurs under the principle of complete randomness, but this principle always does not hold true
Deniz et al (Gomez-Deniz, Vazquez-Polo, and Garcia 2017) introduced a simple count distribution (namely Modified Borel- Tanner (MBT) distribution) which has some eye catching properties like: (I) the distribution consists of one parameter; (II) it is one of the member of exponential family of distributions; (III) it belongs to the class of power series distribution; (IV) it is infinitely divisible; (V) it is unimodal; and (VI) variance larger than the mean, indicating that the one-parameter MBT distribution may be useful to model over-dispersed data
Summary
Poisson model is one of the basic and simplest count data model and most common in practice to deal with count data. Deniz et al (Gomez-Deniz, Vazquez-Polo, and Garcia 2017) introduced a simple count distribution (namely Modified Borel- Tanner (MBT) distribution) which has some eye catching properties like: (I) the distribution consists of one parameter; (II) it is one of the member of exponential family of distributions; (III) it belongs to the class of power series distribution; (IV) it is infinitely divisible; (V) it is unimodal; and (VI) variance larger than the mean, indicating that the one-parameter MBT distribution may be useful to model over-dispersed data. The motivation behind proposing the zero-inflated version of MBT model is that; it consists of only one parameter, the probabilities of the model are monotonically decreasing in x, it is an over-dispersed model and it has very simple closed form expressions which are easy to deal with. Mixing a distribution degenerate at zero with a baseline MBT distribution, we will propose the zero-Inflated Modified Borel–Tanner (ZIMBT) model given by. An application of the proposed model on a real data is shown in section 4 followed by concluding remarks in the last section 5
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
